The rumours of a takeover proposal from JC Flowers, the private equity firm of the former Goldman Sachs deal maker, saw shares rise 22 cents to $3.90.
But Ceberus and other bidders are thought to be keen on breaking up the bank whereas JC Flowers wants to keep it together, according to reports in the Guardian.
Northern Rock did not comment on the events but had previously stated that there was no definite outcome to the talks and there was not even a price on offer from any suitors.
A rise in shares prices at the bank follows bad news last night, that the director general of the Confederation of British Industry (CBI), Richard Lambert, slammed the British system of regulation.
Mr Lambert told City AM: "A run on the bank is something that happens in a banana republic."